The Guardian newspaper said the cables described training for members of the Rapid Action Battalion as being in "investigative interviewing techniques" and "rules of engagement."
One cable notes that U.S. training for the battalion in counterterrorism would be illegal under U.S. law because of human rights violations.
The newspaper said the battalion has been accused by human rights activists of being a "death squad" responsible for more than 1,000 extra-judicial killings since it was established in 2004. In March, the battalion's leader said it had killed 622 people in "crossfire."
The RAB's use of torture has also been exhaustively documented by human rights groups, the Guardian said. In addition, officers from the paramilitary force are alleged to have been involved in kidnap and extortion, and are frequently accused of taking large bribes in return for carrying out killings.
However, the cables reveal that British and Americans officials favor bolstering the force to strengthen counter-terrorism operations in Bangladesh. One cable describes U.S. Ambassador James Moriarty as saying the battalion is the "enforcement organization best positioned to one day become a Bangladeshi version of the U.S. Federal Bureau of Investigation."
The British training began three years ago, The Guardian said, quoting the cables.
Asked by The Guardian about the training for the RAB, the Foreign Office said the UK government "provides a range of human rights assistance" in the country. However, the RAB's head of training, Mejbah Uddin, told the newspaper that he was unaware of any human rights training since he was appointed last summer.
In the most recent killings, the battalion reported that it had shot three men in separate incidents on Tuesday.